Dynamics of the Secant map near infinity
We investigate the root finding algorithm given by the Secant method applied to a real polynomial p of degree k as a discrete dynamical system defined on R2. We extend the Secant map to the real projective plane RP2. The line at infinity ℓ∞ is invariant, and there is one (if k is odd) or two (if k i...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:274786 |
| Acceso en línea: | https://ddd.uab.cat/record/274786 https://dx.doi.org/urn:doi:10.1080/10236198.2022.2044476 |
| Access Level: | acceso abierto |
| Palabra clave: | Root finding algorithms Iteration Secant method |
| Sumario: | We investigate the root finding algorithm given by the Secant method applied to a real polynomial p of degree k as a discrete dynamical system defined on R2. We extend the Secant map to the real projective plane RP2. The line at infinity ℓ∞ is invariant, and there is one (if k is odd) or two (if k is even) fixed points at ℓ∞. We show that these are of saddle type, and this allows us to better understand the dynamics of the Secant map near infinity. |
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